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This paper discusses a design method for controlling a single-input single-output linear time-invariant sampled-data multirate control system, where the sampling interval of a plant output is longer than the holding interval of a control input. In such a sampled-data control system, the control input can be changed between the sampling instants. Hence, even if the sampled output converges to the reference input, the intersample output may oscillate. Such an intersample oscillation is eliminated when the control input is constant. In a conventional method, a control law is extended using an additional signal which is independent of the reference response in the discrete time, and the additional signal is designed so that the control input is constant in the steady state. The conventional method is designed based on the transfer function model, on the other hand, the proposed method is designed using the state-space model. Furthermore, a new design method of the additional input is proposed using the input redundancy which is defined by strongly input redundant or weakly input redundant. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.

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The present paper discusses a design method for a single-input single-output linear time-invariant dual-rate sampled-data control system, where the sampling interval of a plant output is longer than the holding interval of a control input. In such a control system, intersample output oscillation, called ripple, can occur even if the sampled output converges to the reference input. In order to resolve this problem, two design methods have been proposed such that the existing sampled output response is maintained: an open-loop system design method and a closed-loop system design method. However, the open-loop design method cannot be applied to systems for which the gain matrix of the control input is full rank. On the other hand, the closed-loop design method can be used for such systems, but the sampled output response is maintained only in the steady state. The present study proposes a new closed-loop design method in which ripples are eliminated and both the transient and steady-state responses are maintained. The effectiveness of the proposed method is demonstrated through numerical examples.

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